An alga is a simple type of plant.  It is believed that the oil we get from the ground was formed originally from Algae, and was accumulated in the bodies of small sea animals.  This is not the only theory of oil formation, and certainly the whole process of the formation of crude oil is complicated.

Many fish are high in oil.  This also comes through the food chain from Algae.   It makes good sense to use the algae directly.  This has been done on an increasing scale.

Cost

At present the cost of producing and extraction oil from Algae is generally too high to be competitive with crude oil.

However, there are a lot of people working on many different ways of making it cheaper.

One form of extraction is to break down the cellulose cell walls of the algae into simpler sugars so the oil can come out and be separated simply because it floats on the surface of the water.

The remainder of the plant can then be processed into Ethanol.  The biggest problem with this seemingly simple approach is the cost of the enzymes.

Enzyme Cost

The same problem had been the case with turning biomass into ethanol.  But with modern methods of producing enzymes the cost has been brought down to an acceptable level.  The enzymes needed to break down the cell walls of algae are similar, and the same effort could bring down the cost of these enzymes as well.

Capital Cost

Another problem that Algae production has had is the high capital cost of setting up the algae farms.  Much of this is due to the fact that most systems rely on a pure, or nearly pure, strain of algae.  This means that it has to be grown in enclosed vessels.  (These often look like plastic bags.)

A system using mixed strains could be grown in open ponds at much lower cost.  However, the yields from these cultures are likely to be lower, and the processing cost potentially higher.